Zero-field muon-spin relaxation measurements of the frustrated triangular quantum magnet AgNiO2 are consistent with a model of charge disproportionation that has been advanced to explain the structural and magnetic properties of this compound. Below an ordering temperature of TN=19.9(2) K we observe six distinct muon precession frequencies, due to the magnetic order, which can be accounted for with a model describing the probable muon sites. The precession frequencies show an unusual temperature evolution which is suggestive of the separate evolution of two opposing magnetic sublattices.